A string is producing transverse vibration whose equation is $y = 0.021\;\sin (x + 30t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times {10^{ - 4}}\,kg/m,$ then the tension in the string in $N$ will be
Medium
Download our app for free and get started
(d) $y = 0.021\sin (x + 30t)$==> $v = \frac{\omega }{k} = \frac{{30}}{1} = 30\,m/s$.
Using, $v = \sqrt {\frac{T}{m}} \Rightarrow 30 = \sqrt {\frac{T}{{1.3 \times {{10}^{ - 4}}}}} \Rightarrow T = 0.117\,N$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two vibrating tuning forks produce progressive waves given by ${Y_1} = 4\sin 500\pi t$ and ${Y_2} = 2\sin 506\pi t.$ Number of beats produced per minute isView Solution
- 2The equation $y = 0.15\sin 5x\cos 300t$, describes a stationary wave. The wavelength of the stationary wave is .... $m$View Solution
- 3The mass per unit length of a uniform wire is $0.135\, g / cm$. A transverse wave of the form $y =-0.21 \sin ( x +30 t )$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x \times 10^{-2} N$. Value of $x$ is . (Round-off to the nearest integer)View Solution
- 4View SolutionWhen sound waves travel from air to water, which of the following remains constant
- 5$A$ steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wire up and down. $A$ standing wave with three antinodes is created when the spring is stretched by $4.0\, cm$. What stretch of the spring produces a standing wave with two antinodes with same frequency ... $cm$ ?View Solution
- 6The standing wave in a medium is expressed as $y=0.2 \sin (0.8 x) \cos (3000 t) \,m$. The distance between any two consecutive points of minimum or maximum displacement isView Solution
- 7A tuning fork of known frequency $256\,Hz$ makes $5$ beats per second with the vibrating string of a guitar. The beat frequency decreases to $2$ beats per second when the tension in the guitar string slightly increased. The frequency of the guitar string before increasing the tension was ..... $Hz$View Solution
- 8It takes $2.0$ seconds for a sound wave to travel between two fixed points when the day temperature is ${10^o}C.$ If the temperature rise to ${30^o}C$ the sound wave travels between the same fixed parts in ...... $sec$View Solution
- 9Two travelling waves ${y_1} = A\sin [k(x - c\,t)]$ and ${y_2} = A\sin [k(x + c\,t)]$ are superimposed on string. The distance between adjacent nodes isView Solution
- 10View SolutionSpeed of sound at constant temperature depends on